Urbana Campus Research Calendar (OVCRI)

Speaker: Jia Wang
Title: Generalized Poincaré inequality for quantum Markov semigroups 

Abstract: We establish a noncommutative Poincaré inequality for quantum Markov semigroups assuming only a spectral gap. In the tracial setting, for trace-symmetric semigroups, the proof technique includes Markov dilations to obtain chain-rule estimates for Dirichlet forms. We then extend the result to σ-finite von Neumann algebras under GNS detailed balance, using Haagerup’s reduction and Kosaki interpolation to transfer functional inequalities from the tracial to the non-tracial setting. As applications, we recover noncommutative Khintchine and sub-exponential concentration inequalities. 

This is the weekly seminar of the Quantum Working Group in the Department of Mathematics. For questions, please reach out to Marius Junge, Gabriele La Nave, Felix Leditzky, or Amanda Young.